This invention relates generally to grazing incidence optics and more particularly to a diffraction surface grating for obtaining stigmatic imaging.
While the use of uniform curvature concave gratings in grazing incidence optics is well known for focusing both near and remote sources of radiation in the region of the electromagnetic spectrum which includes extreme ultraviolet and soft X-ray radiation, imaging and/or spectral analysis of such radiation is made difficult by the requirement of grazing angle incidence to achieve reasonable reflected intensities, the reason being that such apparatus is unable to focus a plurality of parallel incident rays at these lower wavelengths to a sharp focus which is vitally necessary for the task intended. Various configurations of single uniform curvature diffraction surfaces and combinations thereof have been tried to obtain a sharp focus of the source image but have met with little success. A single concave grating has been used, for example in space experiments at wavelengths from 400 A down to 50 A with a collecting area consisting of the directly illuminated part of the grating, but spatial imaging was marginal. More recently the collecting area has been increased in some instances by using a Wolter lens to form an image of which the central portion serves as the source for a concave grating with the lens and grating both operating at grazing incidence, with the final image being built up by scanning. The use of axially symmetric gratings to make efficient use of the axial symmetry of a preceding collecting element has been further proposed.
Only recently have machining techniques advanced to the stage where non-uniform curvatures can be produced on a body surface and diffraction rulings formed thereon.
Accordingly, it is an object of the present invention to provide a new and improved diffraction surface grating;
Another object of the present invention is to provide an aspheric diffraction surface grating for collecting radiation for imaging and/or spectral analysis;
Still another object of the present invention is to provide a concave diffraction surface grating for focusing short wavelength radiation;
A further object of the present invention is to provide a diffraction surface grating for focusing radiation from both near and far sources of electromagnetic energy whose wavelengths are in the region of extreme ultraviolet and soft X-ray radiation.
Briefly, these and other objects are obtained by the subject invention which comprises an aspheric grazing incidence grating surface having a surface of revolution described by a curve which does not have a constant radius of curvature, but is defined by the relationship ##EQU1##
where m is the diffraction order, .lambda. is the wavelength, .sigma. is the grating ruling interval, x and z are cartesian coordinates of a general point on the diffraction surface described by the curve 20 relative to x and z coordinate axes, .theta..sub.r is the angle that a vector r from the origin to the general point makes with the z axis, and .theta..sub.n is the angle a vector normal to the surface at the general point makes with the z axis. The above equation yields the following solution for constantly spaced rulings .sigma..sub.0 on the surface: ##EQU2## where A=(m.lambda./.sigma..sub.0).sup.2. For a condition of a constant ruling interval .sigma.' along the z axis where .sigma.'=.sigma..sub.0 [1+(dx/dz).sup.2 ].sup.1/2 the following solution obtains: EQU (dx/dz)=x.sup.-1 [(1-A.sup.1/2)(x.sup.2 +z.sup.2).sup.1/2 -z]
where A=(m.lambda./.sigma.').sup.2. When the above relations are observed between the coordinates x and z for a given wavelength, the latter equations define respective families of surfaces which will diffract parallel waves to a sharp focus and vice versa.